Computing the Rank Profile Matrix

The row (resp. column) rank profile of a matrix describes the staircase shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank profiles of a matrix as well as those of all of its leading sub-matrices, in the same time as state of the art Gaussian elimination algorithms. Here we first study the conditions making a Gaus-sian elimination algorithm reveal this information. Therefore, we propose the definition of a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We also explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. As a consequence, we show that the classical iterative CUP decomposition algorithm can actually be adapted to compute the rank profile matrix. Used, in a Crout variant, as a base-case to our ISSAC'13 implementation, it delivers a significant improvement in efficiency. Second, the row (resp. column) echelon form of a matrix are usually computed via different dedicated triangular decompositions. We show here that, from some PLUQ decompositions, it is possible to recover the row and column echelon forms of a matrix and of any of its leading sub-matrices thanks to an elementary post-processing algorithm

A survey of parallel algorithms for fractal image compression

This paper presents a short survey of the key research work that has been undertaken in the application of parallel algorithms for Fractal image compression. The interest in fractal image compression techniques stems from their ability to achieve high compression ratios whilst maintaining a very high quality in the reconstructed image. The main drawback of this compression method is the very high computational cost that is associated with the encoding phase. Consequently, there has been significant interest in exploiting parallel computing architectures in order to speed up this phase, whilst still maintaining the advantageous features of the approach. This paper presents a brief introduction to fractal image compression, including the iterated function system theory upon which it is based, and then reviews the different techniques that have been, and can be, applied in order to parallelize the compression algorithm

Benchmark based on application signature to analyze and predict their behavior

Currently, there are benchmark sets that measure the performance of HPC systems under specific computing and communication properties. These benchmarks represent the kernels of applications that measure specific hardware components. If the user’s application is not represented by any benchmark, it is not possible to obtain an equivalent performance metric. In this work, we propose a benchmark based on the signature of an MPI application obtained by the PAS2P method. PAS2P creates the application signature in order to predict the execution time, which we believe will be very adjusted in relation to the execution time of the full application. The signature has two performance qualities: the bounded time to execute it (a benchmark property) and the quality of prediction. Therefore, we propose to extend the signature by giving the benchmark capacities such as the efficiency of the application over the HPC system. The performance metrics will be performed by the benchmark proposed. The experimentation validates our proposal with an average error of prediction close to 7%.Instituto de Investigación en Informátic

Geometric Random Inner Products: A New Family of Tests for Random Number Generators

We present a new computational scheme, GRIP (Geometric Random Inner Products), for testing the quality of random number generators. The GRIP formalism utilizes geometric probability techniques to calculate the average scalar products of random vectors generated in geometric objects, such as circles and spheres. We show that these average scalar products define a family of geometric constants which can be used to evaluate the quality of random number generators. We explicitly apply the GRIP tests to several random number generators frequently used in Monte Carlo simulations, and demonstrate a new statistical property for good random number generators

Learning from the Success of MPI

The Message Passing Interface (MPI) has been extremely successful as a portable way to program high-performance parallel computers. This success has occurred in spite of the view of many that message passing is difficult and that other approaches, including automatic parallelization and directive-based parallelism, are easier to use. This paper argues that MPI has succeeded because it addresses all of the important issues in providing a parallel programming model.Comment: 12 pages, 1 figur

Numerical electrokinetics

A new lattice method is presented in order to efficiently solve the electrokinetic equations, which describe the structure and dynamics of the charge cloud and the flow field surrounding a single charged colloidal sphere, or a fixed array of such objects. We focus on calculating the electrophoretic mobility in the limit of small driving field, and systematically linearise the equations with respect to the latter. This gives rise to several subproblems, each of which is solved by a specialised numerical algorithm. For the total problem we combine these solvers in an iterative procedure. Applying this method, we study the effect of the screening mechanism (salt screening vs. counterion screening) on the electrophoretic mobility, and find a weak non-trivial dependence, as expected from scaling theory. Furthermore, we find that the orientation of the charge cloud (i. e. its dipole moment) depends on the value of the colloid charge, as a result of a competition between electrostatic and hydrodynamic effects.Comment: accepted for publication in Journal of Physics Condensed Matter (proceedings of the 2012 CODEF conference